#Contents# * table of contents {:toc} ## Definition ## Given a [[sequentially Cauchy complete Archimedean ordered field]] $\mathbb{R}$ and a function $f:\mathbb{R} \to \mathbb{R}$, the type of antiderivatives of $f$ is the [[fiber]] of the [[Newton-Leibniz operator]] at $f$: $$antiderivatives(f) \coloneqq \sum_{g:D^1(\mathbb{R}, \mathbb{R})} \tilde{D}(g) = f$$ An __antiderivative__ is a term of the above type. ## See also ## * [[differentiable function]] * [[derivative]]